The spurious resonance disease and how to cure it: application to the seismic response of a canyon

TL;DR

This paper investigates the spurious resonance problem in boundary integral equation methods for wave scattering and proposes a combined approach that eliminates these false resonances, aligning solutions with exact results.

Contribution

The paper introduces a novel combined BIE method that removes spurious resonances, improving the accuracy of wave scattering solutions compared to traditional methods.

Findings

Traditional BIE methods produce spurious resonances.

Combining two BIE methods eliminates these false resonances.

The new approach matches the exact solution without spurious effects.

Abstract

Three types of boundary integral equation (BIE) methods are employed to obtain closed-form solutions of a wave-scattering problem which are compared to the exact, closed-form (reference), solution deriving from the separation-of-variables technique. The problem involves either Dirichlet (D) or Neumann (N) boundary conditions (BC) for a scatterer that is a circular cylinder submitted to one or two incident waves. The three BIE methods lead to different expressions for the traction (for D-BC) or boundary displacement (for N-BC) by which numerous resonances are predicted whose frequency of occurrence differs from one method to another. This is interpreted as being the sign that the three methods are generally-defective and the resonances are 'spurious'. This 'disease' is cured by combining two BIE into one in such a way that the resulting BIE gives rise to a closed-form solution identical to the exact reference solution devoid of spurious resonances.